If you are settled and have a job where you are now living would you want to move? If the kids are in school and settled right now would more changes benefit them? If as you mentioned earlier she changes her mind and wants to move again then what? You follow her around for the rest of your life?
From what I've read so far you appear to be the stable one at this time and she is a bit all over the place trying to find herself and figure herself out. Eventually she will ( hopefully) settle more and be more balanced. Too me then moving if you all want to would be something to discuss. If she I just running to get away all the problems will keep following her until she deals with them.
What happens if at some point you decide to date and meet someone you like. Most likely they will not want to follow your ex wife every time she wants to move.
I think if she did decide to move it wouldn't take long for her to decide she wants to move again if she has issues with her parents. You have already said this was likely. My advice to you would be to think long and hard about where you want to live and where you think life would be best for you and your kids.
Me 52 H 44 T9 M 5 BD 12/11 H split 8/12 OW moved in 12/12 OW gone for good 6/14 We get closer again 9/14 SD 13 Me 4 Grown
Accept what is...let go of what was and have faith in what will be.